I have been watching kickboxing for some years now particularly the Glory Championships that is in the cable channel. So many fights I have seen were fighters with no more stamina when it comes to round 2. They are like fighting cocks in the first round with so much action but they run out of steam. But one fighter that has good stamina is Saulo Cavalari who is champion in his category maybe because of his strength and lasting power.
Now the question is how do you build up stamina that will last you for 5 rounds?
The stamina or the resistance which a kick boxer may be manifesting is firstly developed through a practice by conditioning his heart for it and by perserving it by fighting in a smart and intelligent way. What I mean for this is stamina remains effective if the fighter has a good technique not to totally exhausting it by playing smartly.
The kind of training the boxer is subjected matters a lot in building stamina to last the rounds. Its okay to train towards winning tournament but there is another aspect of training needed to develop stamina and that is one targeted at developing the body to take punches, heavy or light. A boxer should be trained on how to absorb beating if the fight becomes tough.
Endurance exercises build up lot of stamina. One has to have good lungs capacity as well. I strongly believe that despite all the routine exercises Yoga and meditation can really be a bonus on mastering focus, agility, flexibility and breathing capacity.
As others have said, to be able to build up your endurance then you are going to have to work on your core strength rather than any sort of weight training. Running, walking, jogging and skipping...all improve a fighters stamina and having boxed myself in the past I know only too well how hard (and boring) it can be, and I would assume it's the same for any fighter involved in combat sports.
The glamorous side is the work you do inside the gym and in the ring, but I can tell you that getting up at 4AM to go for a 10KM run every day is soul destroying sometimes. The results in the actual fight make it all worthwhile, but when you're actually doing it you do tend to wish you'd picked another sport to compete in!